Question: Multiply and simplify the following complex numbers: $({-4-5i}) \cdot ({1-i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-4-5i}) \cdot ({1-i}) = $ $ ({-4} \cdot {1}) + ({-4} \cdot {-i}) + ({-5i} \cdot {1}) + ({-5i} \cdot {-i}) $ Then simplify the terms: $ (-4) + (4i) + (-5i) + (5i^2) $ Imaginary unit multiples can be grouped together. $ -4 + (4 - 5)i + 5 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -4 + (4 - 5)i - 5 $ The result is simplified: $ (-4 - 5) + (-1i) = -9-i $